Problem: Solve for $x$. Enter the solutions from least to greatest. $(3x -6)(-x +3)=0$ $\text{lesser }x = $
Solution: For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(3x -6)(-x +3)=0$. So either $(3x -6)=0$ or $(-x +3)=0$ : $\begin{aligned} (1)&&3x -6&=0 \\\\ &&3x&=6 \\\\ &&x&=2 \end{aligned}$ $\begin{aligned} (2)&&-x +3&=0 \\\\ &&-x &= -3 \\\\ &&x&=3 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= 2 \\\\ \text{greater } x &= 3 \end{aligned}$